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Surface Area of a Sphere

Surface Area of a Sphere

Volume of a sphere

The formula for the surface area of a sphere is:

`A = 4pir^2`

Note that the answer will be in square units eg cm2 or m2, as the answer is an area.

Example 1

The diameter of a sphere is measured as 12cm. What, to 2 decimal places, is the surface area of the sphere?

For a Sphere Area `= 4pir^2`
Substitute (`r=frac(1)(2) xx 12`) `A` `= pi(6)^2`
Divide both sides by 100 `A` `= 113.0973`

Answer: 113.10 cm2

Example 2

An experimental package is to be lowered into the sea to investigate global warming at the bottom of the ocean. Part of the experiment includes a hemisphere which is to be covered in a special coating. The hemisphere is solid, is of a constant thickness throughout and has no holes or apertures. The coating costs £4.50 per square centimetre.

The hemisphere has an external diameter of 40cm and has a constant thickness of 5mm. If the hemisphere has to be totally covered, what will the cost of the coating be?

Total surface area of a hemisphere

Total Surface Area = Surface area outside + surface area inside + rim

Radius of outside = 40 ÷ 2 = 20cm

Radius of inside = 20 - 5 = 15cm

Area Sphereoutside Area `= 4pir^2`
Substitute `A` `= 4pi(20)^2`
`= 5026.55`

Area Sphereinside Area `= 4pir^2`
Substitute `= 4pi(15)^2`
`= 2827.43`

Area Rimouter Area `= pir^2`
Substitute `= pi(20)^2`
`= 1256.64`

Area Riminner Area `= pir^2`
Substitute `= pi(15)^2`
`= 706.86`

Total Surface Area

= 5026.55 + 2827.43 + (1256.64 - 706.86)

= 8403.76

Total Cost = 8403.76 x £4.50 = £37,816.92

Answer: £37816.92